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NeX [460]
2 years ago
7

Use the drawing tool(s) to form the correct answer on the provided graph.

Mathematics
1 answer:
AlekseyPX2 years ago
5 0

The solutions to the system of equations are (-2,-6) and (4,6)

<h3>How to determine the system of equations?</h3>

We have:

-2x + y = -2

y = -\frac12x^2 + 3x + 2

Next, we plot the graph of both functions.

From the attached graph, the equations intersect at (-2,-6) and (4,6)

Hence, the solutions to the system of equations are (-2,-6) and (4,6)

Read more about system of equations at:

brainly.com/question/21405634

#SPJ1

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A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and
goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}

Solve for S(t):

\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}

e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}

The left side is the derivative of a product:

\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}

Integrate both sides:

e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt

e^{t/800}S(t)=64e^{t/800}+C

S(t)=64+Ce^{-t/800}

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

0=64+C\impleis C=-64

and so (b) the amount of sugar in the tank at time t is

S(t)=64\left(1-e^{-t/800}\right)

As t\to\infty, the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

7 0
3 years ago
Someone annnnswer pls
cupoosta [38]

Answer:

t = 16

Step-by-step explanation:

Hope this helped :]

4 0
3 years ago
Read 2 more answers
What is the system of inequalities associated with the following graph
Fynjy0 [20]

Answer:

y<3

x+y≥1

This is the system of inequalities which will give you the result shown in the graph

Answered by GAUTHMATH

6 0
3 years ago
Jon makes a map of his neighborhood for a presentation. The scale of his map is 1 inch:125 feet. How many feet do 4 inches
kap26 [50]

Answer:

Part A) 500\ ft

Part B) 2\ in

Step-by-step explanation:

we know that

The scale of the map is \frac{1}{125} \frac{in}{ft}

That means

1 in on the map represent 125 ft in the real

Part A) How many feet do 4 inches

using proportion

\frac{1}{125} \frac{in}{ft}=\frac{4}{x} \frac{in}{ft}\\ \\x=125*4\\ \\x=500\ ft

Part B) Jon lives 250 feet away from Max. How many inches separate Jon’s home from Max’s on the map?

using proportion

\frac{1}{125} \frac{in}{ft}=\frac{x}{250} \frac{in}{ft}\\ \\x=250/125\\ \\x=2\ in

5 0
3 years ago
Last year Kristen read one fourth as many biographies as mysteries and eighteen more science fiction books than biographies. The
Minchanka [31]
Ans: She read 35 books in all.

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